Fluid Dynamics and Stream Function

Satisfactory Essays
Q2 b) Consider the velocity field V = Ax/(x²+y²)i + Ay/(x²+y²)j in the xy plane, where A = 10 m²/s, and x and y are measured in meters.
i) Show this is an incompressible flow field. ii) Derive an expression for the fluid acceleration. iii) Evaluate the acceleration along the x axis, the y axis, and along a line defined by y = x. (14 marks)

Question 1 ( 15 markah )
a) Define and explain briefly the following :
i) velocity potential, f (x,y) ( 4 markah ) ii) stream function, y (x,y) ( 4 markah )

b) If the expression for stream function is described by y (x,y) = x3 – 3 xy2 , determine whether flow is rotational or irrotational. If the flow is irrotational, then determine the velocity potential, f and velocity vector, V. ( 7 markah )

Question 1
b) The velocity vector in a certain two-dimensional flow field is given by the equation;
V (x,y) = (x2 – y2 + x) i – (2xy + y) j

i) show that the continuity equation is satisfied ii) is this an irrotational flow field? Justify your answer with the necessary calculations. iii) determine the corresponding stream function iv) sketch several streamlines passing through the origin (12 marks)

Question 1
a) i) Define ‘potential flow’. ii) Describe the governing equation for ‘potential flow’ (8 marks)

b) Consider the flow field given by V = xy2i – 1/3(y3)j + xyk

i) Derive an expression for the fluid acceleration. ii) Evaluate the velocity along the x axis. iii) Evaluate the acceleration along the y axis. iv) Determine the number of dimensions of the flow. (12 marks)

Q2 In a two-dimensional incompressible flow the fluid velocity components are given by u = x - 4y and v = - y - 4x.

(i) Show that the flow satisfies the continuity equation. (ii) Obtain the expression for the stream function. (iii) Obtain the expression for the velocity potential. (iv) Show that the flow is potential. (15 marks)

You May Also Find These Documents Helpful

  • Good Essays

    Fluid Dynamics and Pressure

    • 4443 Words
    • 18 Pages

    Chapter 3: FLUID FLOW CHAPTER THREE FLUID FLOW 3.1 3.2 3.3 3.4 3.5 Fluid Flow Unit Pump Test Unit Hydraulics bench and accessories Flow Curve Determination for Non-Newtonian Fluids Fixed and Fluidized Bed Facts which at first seem improbable will, even in scant explanation, drop the cloak which has hidden them and stand forth in naked and simple beauty. GALILEO GALILEI 1 3.1. FLUID FLOW UNIT Keywords: Pressure loss, straight pipe, pipe bend, orifice meter, venturi meter…

    • 4443 Words
    • 18 Pages
    Good Essays
  • Powerful Essays

    computational fluid dynamics

    • 2989 Words
    • 12 Pages

    th th Proceedings of the 37th National & 4th International Conference on Fluid Mechanics and Fluid Power Proceedings of the 37 International &16-18, 2010, IIT Madras, Chennai, India. 4 National Conference on Fluid December Mechanics and Fluid Power FMFP10 - TM - 08 FMFP2010 December 16-18, 2010, IIT Madras, Chennai, India FMFP2010 CFD BASED FLOW ANALYSIS OF CENTRIFUGAL PUMP S R Shah S V Jain M Tech in Thermal Engineering Mechanical Engineering Department Institute of…

    • 2989 Words
    • 12 Pages
    Powerful Essays
  • Powerful Essays

    wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetic, and fluid dynamics. Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange. Figure 1-Wave Diffusion Wave equation has many applications…

    • 1680 Words
    • 7 Pages
    Powerful Essays
  • Good Essays

    STUDI DI UDINE Dottorato in Tecnologie Chimiche ed Energetiche FLUID DYNAMIC MODELLING OF WIND TURBINES sec. D Vr 0 D Vt Vz Vr Vt 3 Relatori: Prof.Ing. Lorenzo BATTISTI Prof.Ing. Piero PINAMONTI Dottorando: Dott.Ing. Luca ZANNE Udine 21 Maggio 2010 Summary Introduction PART I : HAWT analysis HAWT Fluid dynamics A turbomachinery approach Inverse design Summary PART II : VAWT analysis VAWT fluid dynamics VAWT experimental analysis VAWT free vortex wake Results and conclusions…

    • 5982 Words
    • 24 Pages
    Good Essays
  • Good Essays

    MANUAL DESIGN OF MULTIPLE-PIPE SLUG CATCHERS DEP 31.40.10.12-Gen. July 1998 DESIGN AND ENGINEERING PRACTICE This document is confidential. Neither the whole nor any part of this document may be disclosed to any third party without the prior written consent of Shell International Oil Products B.V. and Shell International Exploration and Production B.V., The Hague, The Netherlands. The copyright of this document is vested in these companies. All rights reserved. Neither the whole nor any part of…

    • 11494 Words
    • 46 Pages
    Good Essays
  • Satisfactory Essays

    Definition of Aerodynamics: a branch of dynamics that deals with the motion of air and other gaseous fluids and with the forces acting on bodies in motion relative to such fluids http://www.merriam-webster.com/dictionary/aerodynamics Other: aerios, concerning the air, and dynamis, which means force. http://www.grc.nasa.gov/WWW/K-12/airplane/bga.html Bernoulli's Principle: • The relationship between the velocity and pressure exerted by a moving liquid • States that for an inviscid…

    • 309 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Exercise 5: Cardiovascular Dynamics: Activity 1: Studying the Effect of Blood Vessel Radius on Blood Flow Rate Lab Report Pre-lab Quiz Results You scored 100% by answering 5 out of 5 questions correctly. 1. Blood flow is measured in You correctly answered: b. ml/min. 2. Which of the following has the greatest effect on blood flow? You correctly answered: a. blood vessel radius 3. Which of the following would not result in a decrease in the blood vessel radius? You correctly answered: c. vasodilation…

    • 635 Words
    • 3 Pages
    Good Essays
  • Better Essays

    Computational Fluid Dynamics Analysis Of Wind Turbine Blade Gopinath.c¹, Kishore kumar.r2 Mechanical department Third year(2010-2014) Ranippettai engineering college. Email ID: gopinath4010gmail.com ABSTRACT: A wind turbine is a rotary device that extracts energy from the wind. Wind energy has been shown to be one of the most viable sources of renewable energy. With current technology, the low cost of wind energy is competitive with more conventional…

    • 3441 Words
    • 21 Pages
    Better Essays
  • Powerful Essays

    10 Final code 11 Implicit Method 15 Final Code 16 Numerical results 18 Analysis of the Numerical results 23 Conclusion 24 References 25 Introduction Over the years the importance of fluid dynamics has grown exponentially. It represents the theoretical and physical aspects of the fluid in motion, as it flows naturally or when effected by a force. This application can be applied to liquids and gases providing a deeper understanding of pure sciences such as atmospheric, geophysics and…

    • 4764 Words
    • 20 Pages
    Powerful Essays
  • Satisfactory Essays

    Tutorial 5&6: 1. A trickling filter has a diameter of 20 m and a depth of 2.5 m. It is operated with a direct recirculation ratio of 1.0, and the influent sewage flow rate is 3 ML/d. Influent BOD to the primary tank is 200 mg/L, and the BOD removal efficiency in that tank is 35 percent. Compute the organic load on the trickling filter. 2. A grit of specific gravity 2.8 flows into a grit chamber, 1.5-m wide, 10.5-m long and 2.5-m deep. The flow-rate of wastewater into the chamber is 2 m3/s.…

    • 280 Words
    • 2 Pages
    Satisfactory Essays